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C25⋊((C11⋊D11)⋊C3) #31827588

order18150
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C11

Aliases

unambiguous semidirect productC25⋊((C11⋊D11)⋊C3)
unambiguous semidirect product(C11⋊D275)⋊C3

Splittings

Fitting, derived, HallC112×C25 ⋊ C2×C3
HallC25×C112⋊C3 ⋊ C2
HallC11⋊D275 ⋊ C3
HallC112⋊C3 ⋊ D25
SylowC112 ⋊ C3×D25
SylowC25 ⋊ (C11⋊D11)⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC112×C25C2×C3
FrattiniC5C5⋊((C11⋊D11)⋊C3)
socleC5×C112C3×D5
LCSG ▷ C112×C25
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 825

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2,4)(3,15,17,7,8,24)(5,23,20,12,13,30)(6,11,21,16,10,22)(9,27,29,18,19,33)(14,28,32,25,26,31)(35,37)(36,40)(38,43)(39,46)(41,49)(42,48)(44,45)(47,53)(50,54)(51,55)(52,57)(56,58);(1,3,9,20,22,31,32,21,30,18,7)(2,5,14,27,8,16,6,15,19,25,12)(4,10,13,24,26,29,33,28,17,23,11)(34,48,58,51,37,40,54,52,43,46,49,47,45,44,53,41,39,38,57,50,36,35,55,56,42)

Polycyclic presentation:

2,3,5,11^2,5|c^5=f^4,c^a=c^4f,d^a=d^10,e^a=e^10,f^a=f^4,d^b=d^7e^5,e^b=d^4e^3

Conjugacy classes & character table

542 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#49137116, #27130822⋊C3, #10624391⋊D25, …
maximal normal subgroup of#49137116, #27130822⋊C3, #10624391⋊D25, …
maximal quotient of(C11⋊Dic275)⋊C3, C2×C25⋊((C11⋊D11)⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 72);