Finite Group Databasebeta

C2×C4×#13063373 #26003206

order11008
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×C4×#13063373

Splittings

FittingC22×C4×Q8×C43 ⋊ C2
SylowC43 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC22×C4×Q8×C43C2
socleC23×C43C25
prime radicalC22×#13063373C2
cosocleC22×C43C26
hypercenterC22×C4×Q8D43
hypocenterC43C2×C4×2−1+4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

11210 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076177);