Finite Group Databasebeta

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Q8×C4⋊C4×D83 #35563702

order21248
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×C4⋊C4×D83

Splittings

FittingQ8×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingQ8×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC23×D83C24
hypercenterQ8×C4⋊C4D83
hypocenterC83C2×Q8×C4⋊C4
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 328866);