Finite Group Databasebeta

C4×#17985731 #31888050

order18176
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#17985731

Splittings

SylowC71 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC2×C42D284
commutatorC4×C71C2×C4×C8
FrattiniC2×C42C22×D71
FittingC42×C8×C71C2
socle, prime radicalC23×C71C2×C22⋊C4
cosocleC2×C42×C71C23
hypercenterC42×C8D71
hypocenterC71C4×Q8⋊C8
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

4592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 60166);