Finite Group Databasebeta

C2×C22⋊Q8×D293 #49172009

order37504
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×C22⋊Q8×D293

Splittings

FittingC2×C22⋊Q8×C293 ⋊ C2
SylowC293 ⋊ C22×C22⋊Q8

Subgroups

subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×C22⋊Q8×C293C2
socleC23×C293C24
prime radicalC24×D293C22
hypercenterC2×C22⋊Q8D293
hypocenterC293C22×C22⋊Q8
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

4144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 17734);