Finite Group Databasebeta

C2×#28414614 #44445246

order29632
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#28414614

Splittings

SylowC463 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D463
commutatorC2×C463C23×C4
FrattiniC22C23×D463
FittingC2×C22⋊C4×C463C2
socleC23×C463C23
prime radicalC24×C463C22
cosocleC22×C463C24
hypercenterC2×C22⋊C4D463
hypocenterC463C2×#117
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Conjugacy classes & character table

4660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 1002);