Finite Group Databasebeta

C2×#32914662 #49148491

order36928
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#32914662

Splittings

SylowC577 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
centerC23C22×D577
commutator, cosocleC22×C577C24
FrattiniC22C23×D577
FittingC22×Q8×C577C2
socle, prime radicalC23×C577C23
hypercenterC22×Q8D577
hypocenterC577C2×C4⋊Q8
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C23 ◁ C22×Q8

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36928

Conjugacy classes & character table

5788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 1091);