Finite Group Databasebeta

C2×#19134917 #25097809

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

Aliases

direct productC2×#19134917

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ C2×#1875

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#117×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063299C2
cosocleC22×C4×C43C24
hypercenterC22×#117D43
hypocenterC43C2×#1875
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#117

2310 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 170780);