Finite Group Databasebeta

C22×#10625000 #15681972

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#10625000

Splittings

SylowC23 ⋊ C22×#107

Subgroups

subgroupG/H
centerC24D92
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×C8×C23C2
socle, prime radicalC24×C23D4
cosocleC2×C4×C23C24
hypercenterC23×C8D23
hypocenterC23C22×#107
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13085);