Finite Group Databasebeta

C2×#20297229 #28383572

order14272
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20297229

Splittings

SylowC223 ⋊ C2×#103

Subgroups

subgroupG/H
centerC23D892
commutatorC4×C223C22×C4
FrattiniC2×C4C22×D223
FittingC22×C8×C223C2
socle, prime radicalC23×C223D4
cosocleC2×C4×C223C23
hypercenterC22×C8D223
hypocenterC223C2×#103
LCSG ▷ C4×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14272

Conjugacy classes & character table

3580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14272, 541);