Finite Group Databasebeta

C2×#26038181 #37507584

order22912
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#26038181

Splittings

SylowC179 ⋊ C2×#330

Subgroups

subgroupG/H
centerC23C22⋊Dic179
commutatorC2×C4×C179C22×C4
FrattiniC42C22×D179
FittingC2×#125×C179C2
socle, prime radicalC23×C179C22⋊C4
cosocleC42×C179C23
hypercenterC2×#125D179
hypocenterC179C2×#330
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22912

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22912, 3094);