Finite Group Databasebeta

C2×#20300898 #28411429

order14656
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20300898

Splittings

SylowC229 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D229
commutatorC2×C229C2×C42
FrattiniC2×C4C22×D229
FittingC22×C8×C229C2
socle, prime radicalC23×C229C2×C4
cosocleC2×C4×C229C23
hypercenterC22×C8D229
hypocenterC229C2×#97
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C22×C4 ◁ C22×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

Conjugacy classes & character table

3688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 497);