Finite Group Databasebeta

← Prev (#32157310) Next (#32157312) →

Q8×(C22⋊D71)⋊C4 #32157311

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×(C22⋊D71)⋊C4

Splittings

FittingQ8×C22⋊C4×C71 ⋊ C2
SylowC71 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C22⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC22×C22⋊D71C23
hypercenterQ8×C22⋊C4D71
hypocenterC71C4×D4×Q8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

3148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 329427);