Finite Group Databasebeta

C2×Q8×#63223 #17898712

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×Q8×#63223

Splittings

SylowC17 ⋊ C2×Q8×M16

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C4×Q8×C17C2
socleC23×C17C23×C4
prime radicalC24×C17C22×C4
cosocleC2×C4×C17C25
hypercenterC22×C4×Q8D17
hypocenterC17C2×Q8×M16
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

2154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033956);