Finite Group Databasebeta

Q8×#14579089 #34304969

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#14579089

Splittings

FittingC42×Q8×C79 ⋊ C2
SylowC79 ⋊ Q8×#104

Subgroups

subgroupG/H
centerC2×C4C22×D316
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC42×Q8×C79C2
socleC22×C79C22×C22⋊C4
prime radicalC2×#11929624C23
cosocleC22×C4×C79C24
hypercenterC42×Q8D79
hypocenterC79Q8×#104
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C42×Q8

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 186268);