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C7×C23⋊(Dic13⋊C3) #38737310

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23⋊(Dic13⋊C3)
unambiguous semidirect productC23⋊(C7×Dic13⋊C3)
unambiguous semidirect productDic299⋊(C3×C7)

Splittings

derived, HallC13×C23 ⋊ C3×C4×C7
HallC7×Dic299 ⋊ C3
HallC7×C23×C13⋊C3 ⋊ C4
HallC7×C13×C23 ⋊ C3×C4
HallDic299 ⋊ C3×C7
HallC23×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ Dic23
HallC7×C23 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×Dic23
HallC13⋊C3 ⋊ C7×Dic23
SylowC23 ⋊ C7×Dic13⋊C3
SylowC13 ⋊ C3×C7×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C7C23⋊(D13⋊C3)
commutator, hypocenterC13×C23C3×C4×C7
FrattiniC2C7×C23⋊(D13⋊C3)
Fitting, socleC2×C7×C13×C23C2×C3
prime radicalC2×C7×C23×C13⋊C3C2
cosocleC2×C13×C23C2×C3×C7
LCSG ▷ C13×C23
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8372

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 29);