Finite Group Databasebeta

C4×#10597435 #14576842

order2432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#10597435

Splittings

FittingC4×#41×C19 ⋊ C2
SylowC19 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C23×D19
commutatorC2×C19C24×C4
FrattiniC22C24×D19
FittingC4×#41×C19C2
socle, cosocleC22×C19C25
prime radicalC2×#10597435C2
hypercenterC4×#41D19
hypocenterC19C4×H(5,𝔽2)
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C4×#41

1660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18073936, #18073939
maximal normal subgroup of#18073936, #18073939

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17717);