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ΓL(1,𝔽8)×C23×Dic13 #38737307

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

Aliases

direct productΓL(1,𝔽8)×C23×Dic13

Splittings

derived, HallC7×C13 ⋊ C3×C4×C23
HallC7×C23×Dic13 ⋊ C3
HallC13×ΓL(1,𝔽8)×C23 ⋊ C4
HallC7×C13×C23 ⋊ C3×C4
HallC7×Dic13 ⋊ C3×C23
HallC13×C23 ⋊ C4×ΓL(1,𝔽8)
HallC13×ΓL(1,𝔽8) ⋊ C4×C23
HallC7×C23 ⋊ C3×Dic13
SylowC13 ⋊ C4×ΓL(1,𝔽8)×C23
SylowC7 ⋊ C3×C23×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C23ΓL(1,𝔽8)×D13
commutator, hypocenterC7×C13C3×C4×C23
FrattiniC2ΓL(1,𝔽8)×C23×D13
Fitting, socleC2×C7×C13×C23C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C23C2
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

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 26);