Finite Group Databasebeta

C2×Q16×C83⋊C8 #35373775

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q16×C83⋊C8

Splittings

SylowC83 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC22×C4D4×D83
commutatorC4×C83C23×C8
FrattiniC42C23×D83
FittingC2×C4×Q16×C83C2
socle, prime radicalC23×C83C4×D4
cosocleC42×C83C24
hypercenterC2×C4×Q16D83
hypocenterC83C2×C8×Q16
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 138939);