Finite Group Databasebeta

C22×C22⋊Dic463 #44445241

order29632
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊Dic463

Splittings

SylowC463 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D463
commutatorC2×C463C23×C4
FrattiniC22C23×D463
Fitting, prime radicalC25×C463C2
socleC24×C463C22
cosocleC22×C463C24
hypercenterC25D463
hypocenterC463C22×C22⋊C4
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C24 ◁ C25

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Conjugacy classes & character table

7432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 997);