Finite Group Databasebeta

C2×#19134654 #25096271

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19134654

Splittings

SylowC43 ⋊ C2×#1815

Subgroups

subgroupG/H
centerC23#13063299
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#131×C43C2
socleC23×C43#121
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC22×#131D43
hypocenterC43C2×#1815
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#131

1374 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 169242);