Finite Group Databasebeta

← Prev (#37528588) Next (#37528590) →

C2×C52×ΓL(1,𝔽8)×D11 #37528589

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×ΓL(1,𝔽8)×D11

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, HallC7×C11 ⋊ C22×C3×C52
HallC2×C52×C7×D11 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC2×C7×D11 ⋊ C3×C52
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C22×C52
HallC52×C7 ⋊ C2×C3×D11
SylowC11 ⋊ C22×C52×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C52×D11

Subgroups

subgroupG/H
center, hypercenterC2×C52ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C22×C3×C52
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C2×C52

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 400);