Finite Group Databasebeta

C42×#63225 #16955404

order4352
isoclinismisoclinic class of Dic34
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC42×#63225

Splittings

SylowC17 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC22×C42C2×D17
commutatorC2×C17C2×C43
FrattiniC24C23×D17
FittingC2×C43×C17C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×C43D17
hypocenterC17C42×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C42 ◁ C2×C43

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90648);