Finite Group Databasebeta

C2×Q8×#6090 #16016401

order3328
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#6090

Splittings

SylowC13 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC2×C13C23×C16
FrattiniC2×C8C23×D13
FittingC2×C8×Q8×C13C2
socle, prime radicalC23×C13C22×C8
cosocleC2×C8×C13C24
hypercenterC2×C8×Q8D13
hypocenterC13C2×Q8×C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323050);