Finite Group Databasebeta

C4⋊Q8×D577 #49148490

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

Aliases

direct productC4⋊Q8×D577

Splittings

FittingC4⋊Q8×C577 ⋊ C2
SylowC577 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
FittingC4⋊Q8×C577C2
prime radicalC22×D577C23
hypercenterC4⋊Q8D577
hypocenterC577C2×C4⋊Q8
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ C4⋊Q8

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18464

Conjugacy classes & character table

4060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 1090);