Finite Group Databasebeta

C8×#66995 #14723198

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#66995

Splittings

FittingC2×C8×Q8×C11 ⋊ C2
SylowC11 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11C8×#137
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 138993);