Finite Group Databasebeta

C22×C22⋊Dic577 #49148397

order36928
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊Dic577

Splittings

SylowC577 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D577
commutatorC2×C577C23×C4
FrattiniC22C23×D577
Fitting, prime radicalC25×C577C2
socleC24×C577C22
cosocleC22×C577C24
hypercenterC25D577
hypocenterC577C22×C22⋊C4
LCSG ▷ C2×C577 ▷ C577
UCSC1 ◁ C24 ◁ C25

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18464

Conjugacy classes & character table

9256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 997);