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C7×C23×Dic13⋊C3 #38737306

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C7×C23)
unambiguous semidirect product(C23×Dic13)⋊(C3×C7)

Splittings

derived, SylowC13 ⋊ C3×C4×C7×C23
HallC7×C23×Dic13 ⋊ C3
HallC7×C23×C13⋊C3 ⋊ C4
HallC7×C13×C23 ⋊ C3×C4
HallC23×Dic13 ⋊ C3×C7
HallC23×C13⋊C3 ⋊ C4×C7
HallC7×Dic13 ⋊ C3×C23
HallC13×C23 ⋊ C3×C4×C7
HallC7×C13⋊C3 ⋊ C4×C23
HallC7×C13 ⋊ C3×C4×C23
HallDic13 ⋊ C3×C7×C23
HallC13⋊C3 ⋊ C4×C7×C23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C23D13⋊C3
commutator, hypocenterC13C3×C4×C7×C23
FrattiniC2C7×C23×D13⋊C3
Fitting, socleC2×C7×C13×C23C2×C3
prime radicalC2×C7×C23×C13⋊C3C2
cosocleC2×C13C2×C3×C7×C23
LCSG ▷ C13
UCSC1 ◁ C2×C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8372

Conjugacy classes & character table

2576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 25);