Finite Group Databasebeta

C2×#26018378 #36469406

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

Aliases

direct productC2×#26018378

Splittings

SylowC89 ⋊ C2×#1394

Subgroups

subgroupG/H
centerC23#15667926
commutatorC2×C4×C89C2×C42
FrattiniC22×Q8C22×D89
FittingC22×#101×C89C2
socleC23×C89#99
prime radicalC24×C89C22⋊C4
cosocleC22×Q8×C89C23
hypercenterC22×#101D89
hypocenterC89C2×#1394
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C24 ◁ C23×Q8 ◁ C22×#101

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84546);