Finite Group Databasebeta

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C3×C7⋊(C23⋊#261) #38737408

order25116
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C13×C23 ⋊ C4
derived, HallC7×C13×C23 ⋊ C3×C4
HallC3×C13×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ #261
HallC13×C23 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ Dic23
HallC7×C23 ⋊ C3×#261
HallC7×C13 ⋊ C3×Dic23
HallC3×C23 ⋊ C7⋊#261
HallC3×C13 ⋊ Dic161
SylowC23 ⋊ C3×C7⋊#261
HallC3×C7 ⋊ C23⋊#261
SylowC13 ⋊ C3×Dic161
SylowC7 ⋊ C3×C23⋊#261

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C23⋊#261)
commutator, hypocenterC7×C13×C23C3×C4
FrattiniC1G
Fitting, socleC3×C7×C13×C23C4
prime radicalC3×C7×C23×D13C2
cosocleC7×C23×D13C2×C3
LCSG ▷ C7×C13×C23
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6279

Conjugacy classes & character table

1941 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 127);