Finite Group Databasebeta

C2×C4×C4⋊Dic283 #49123596

order36224
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic283

Splittings

SylowC283 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D283
commutatorC2×C283C22×C42
FrattiniC23C23×D283
FittingC22×C42×C283C2
socle, prime radicalC24×C283C23
cosocleC23×C283C24
hypercenterC22×C42D283
hypocenterC283C2×C4×C4⋊C4
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36224

Conjugacy classes & character table

9104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 6845);