Finite Group Databasebeta

C2×#26018362 #36469352

order22784
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#26018362

Splittings

SylowC89 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#15667932
commutatorC8×C89C2×C42
FrattiniC22×C8C22×D89
FittingC22×#108×C89C2
socleC23×C89#102
prime radicalC24×C89SD16
cosocleC22×C8×C89C23
hypercenterC22×#108D89
hypocenterC89C2×#1387
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11392

Conjugacy classes & character table

2528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84492);