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C7×C3⋊(C23⋊#261) #38737416

order25116
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C23⋊#261)
unambiguous semidirect productC3⋊(C7×C23⋊#261)
unambiguous semidirect productC23⋊(C7×C3⋊#261)

Splittings

Fitting, socle, HallC3×C7×C13×C23 ⋊ C4
derived, HallC3×C13×C23 ⋊ C4×C7
HallC7×C13×C23 ⋊ Dic3
HallC3×C7×C23 ⋊ #261
HallC13×C23 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ Dic23
HallC7×C23 ⋊ C3⋊#261
HallC7×C13 ⋊ Dic69
HallC3×C23 ⋊ C7×#261
HallC3×C13 ⋊ C7×Dic23
SylowC23 ⋊ C7×C3⋊#261
HallC3×C7 ⋊ C23⋊#261
SylowC13 ⋊ C7×Dic69
SylowC3 ⋊ C7×C23⋊#261

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C23⋊#261)
commutator, hypocenterC3×C13×C23C4×C7
FrattiniC1G
Fitting, socleC3×C7×C13×C23C4
prime radicalC3×C7×C23×D13C2
cosocleC3×C23×D13C2×C7
LCSG ▷ C3×C13×C23
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6279

Conjugacy classes & character table

1953 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 135);