Finite Group Databasebeta

C4×#22604397 #49147802

order36928
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#22604397

Splittings

SylowC577 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D577
commutatorC2×C577C2×C42
FrattiniC23C22×D577
FittingC2×C42×C577C2
socle, prime radical, cosocleC23×C577C23
hypercenterC2×C42D577
hypocenterC577C4×C4⋊C4
LCSG ▷ C2×C577 ▷ C577
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36928

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, 402);