Finite Group Databasebeta

C4⋊C4×Dic38 #14566550

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic38

Splittings

SylowC19 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC4×C4⋊C4×C19C2
socle, prime radical, cosocleC23×C19C24
hypercenterC4×C4⋊C4D19
hypocenterC19Q8×C4⋊C4
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18076712, #18076716, #18076740, …
maximal normal subgroup of#18076712, #18076716, #18076740, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7425);