Finite Group Databasebeta

C2×#28414681 #44445576

order29632
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28414681

Splittings

FittingC2×Q16×C463 ⋊ C2
SylowC463 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D463
commutator, cosocleC4×C463C24
FrattiniC4C23×D463
FittingC2×Q16×C463C2
socleC22×C463C2×D4
hypercenterC2×Q16D463
hypocenterC463C2×#135
LCSG ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Conjugacy classes & character table

3262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 1332);