Finite Group Databasebeta

C2×#19132718 #25011558

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132718

Splittings

SylowC43 ⋊ C2×#1392

Subgroups

subgroupG/H
centerC2×C4#13063240
commutatorC23×C43C2×C42
FrattiniC2×#41C22×D43
FittingC2×C43×#408C2
socleC22×C43#342
prime radicalC22×#41×C43C22
cosocleC2×#41×C43C23
hypercenterC2×#408D43
hypocenterC43C2×#1392
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#408

750 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84529);