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C7×C23×C3⋊#261 #38737415

order25116
automorphism?
homologyAbelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C23C3⋊#261
commutator, hypocenterC3×C13C4×C7×C23
FrattiniC1G
Fitting, socleC3×C7×C13×C23C4
prime radicalC3×C7×C23×D13C2
cosocleC3×D13C2×C7×C23
LCSG ▷ C3×C13
UCSC1 ◁ C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6279

Conjugacy classes & character table

2415 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 134);