Finite Group Databasebeta

C2×Q8×C83⋊C16 #35557886

order21248
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×C83⋊C16

Splittings

SylowC83 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C8C22×D83
commutatorC2×C83C23×C16
FrattiniC2×C8C23×D83
FittingC2×C8×Q8×C83C2
socle, prime radicalC23×C83C22×C8
cosocleC2×C8×C83C24
hypercenterC2×C8×Q8D83
hypocenterC83C2×Q8×C16
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 323050);