Finite Group Databasebeta

C2×#20300953 #28411945

order14656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20300953

Splittings

SylowC229 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D229
commutatorC2×C229C23×C4
FrattiniC22C23×D229
FittingC2×C4⋊C4×C229C2
socle, prime radicalC23×C229C23
cosocleC22×C229C24
hypercenterC2×C4⋊C4D229
hypocenterC229C2×C4×Q8
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C23 ◁ C2×C4⋊C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1013);