Finite Group Databasebeta

C22×C4×C22⋊D19 #14576804

order2432
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×C4×C22⋊D19

Splittings

FittingC24×C4×C19 ⋊ C2
SylowC19 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC23×C4C2×D19
commutatorC2×C19C24×C4
FrattiniC22C24×D19
FittingC24×C4×C19C2
socleC24×C19C23
prime radicalC23×C22⋊D19C2
cosocleC22×C19C25
hypercenterC24×C4D19
hypocenterC19C22×C4×D4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C24×C4

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18073875, #18087960, #18089025
maximal normal subgroup of#18073875, #18087960, #18089025

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17679);