Finite Group Databasebeta

C22×C22⋊Dic41 #14580784

order2624
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊Dic41

Splittings

SylowC41 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D41
commutatorC2×C41C23×C4
FrattiniC22C23×D41
Fitting, prime radicalC25×C41C2
socleC24×C41C22
cosocleC22×C41C24
hypercenterC25D41
hypocenterC41C22×C22⋊C4
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C24 ◁ C25

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 997);