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C11⋊((C13⋊C3)⋊D31) #40998258

order26598
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊((C13⋊C3)⋊D31)
unambiguous semidirect product(C13⋊C3)⋊D341

Splittings

Fitting, socle, derived, HallC11×C13×C31 ⋊ C2×C3
HallC11×C31×C13⋊C3 ⋊ C2
HallD4433 ⋊ C3
HallC31×C13⋊C3 ⋊ D11
HallC11×C13⋊C3 ⋊ D31
HallC13×C31 ⋊ C3×D11
HallC11×C31 ⋊ D13⋊C3
HallC11×C13 ⋊ C3×D31
HallC13⋊C3 ⋊ D341
SylowC31 ⋊ C11⋊(D13⋊C3)
SylowC13 ⋊ C3×D341
SylowC11 ⋊ (C13⋊C3)⋊D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C13×C31C2×C3
LCSG ▷ C11×C13×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 4433

A minimal faithful permutation representation — 2 generators on 55 points:

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

Polycyclic presentation:

2,3,11,13,31|c^a=c^10,d^a=d^12,e^a=e^30,d^b=d^3

Conjugacy classes & character table

1198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26598, 46);