Finite Group Databasebeta

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C23×#11763963 #38737324

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

Aliases

direct productC23×#11763963

Splittings

derived, HallC7×C13 ⋊ C3×C4×C23
HallC23×Dic91 ⋊ C3
HallC23×#63270 ⋊ C4
HallC7×C13×C23 ⋊ C3×C4
HallDic91 ⋊ C3×C23
HallC13×C23 ⋊ ΓL(1,𝔽8)⋊C4
Hall#63270 ⋊ C4×C23
HallC7×C23 ⋊ Dic13⋊C3
SylowC13 ⋊ C23×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C23×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C23#10587722
commutator, hypocenterC7×C13C3×C4×C23
FrattiniC2C23×#10587722
Fitting, socleC2×C7×C13×C23C2×C3
prime radicalC2×C23×#63270C2
cosocleC2×C7×C13C2×C3×C23
LCSG ▷ C7×C13
UCSC1 ◁ C2×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8372

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 43);