Finite Group Databasebeta

C2×Q8×C22⋊D29 #16832964

order3712
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×C22⋊D29

Splittings

FittingC23×Q8×C29 ⋊ C2
SylowC29 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC23×Q8×C29C2
socleC23×C29C24
prime radicalC22×C22⋊D29C22
hypercenterC23×Q8D29
hypocenterC29C2×D4×Q8
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C23×Q8

1568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 17982);