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C3⋊(C7⋊(Dic11⋊C25)) #37528215

order23100
automorphism?
homologyAbelianization (H1) = C4×C25 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C7⋊(Dic11⋊C25))
unambiguous semidirect productC7⋊(C3⋊(Dic11⋊C25))
unambiguous semidirect product(C11⋊C25)⋊Dic21
unambiguous semidirect productDic231⋊C25

Splittings

derived, HallC3×C7×C11 ⋊ C4×C25
HallC3×C7×C11⋊C25 ⋊ C4
HallC7×C11⋊C25 ⋊ Dic3
HallDic231 ⋊ C25
HallC3×C11⋊C25 ⋊ Dic7
HallC11⋊C25 ⋊ Dic21
HallC7×C11 ⋊ Dic3×C25
HallC3×C11 ⋊ C25×Dic7
HallC3×C7 ⋊ Dic11⋊C25
SylowC11 ⋊ C25×Dic21
SylowC7 ⋊ C3⋊(Dic11⋊C25)
SylowC3 ⋊ C7⋊(Dic11⋊C25)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2×C5C3⋊(C7⋊AGL(1,𝔽11))
commutator, hypocenterC3×C7×C11C4×C25
Fitting, socle, prime radical, cosocleC2×C3×C5×C7×C11C2×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Polycyclic presentation:

2,3,5,7,11,2,5|a^2=f,c^5=g,b^a=b^2,d^a=d^6,e^a=e^10,e^c=e^4

Conjugacy classes & character table

810 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 26);