Finite Group Databasebeta

C2×C4×C4⋊#1181 #16835922

order3712
isoclinismisoclinic class of #90796
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊#1181

Splittings

FittingC2×C42×C29 ⋊ C4
SylowC29 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×#1181
commutatorC2×C29C22×C42
FrattiniC22C23×#1181
FittingC2×C42×C29C4
socleC23×C29C22×C4
prime radicalC23×D29C23
cosocleC22×D29C24
hypercenterC2×C42#1181
hypocenterC29C2×C4×C4⋊C4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C2×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 20940);