Finite Group Databasebeta

C2×#11926301 #14563336

order2432
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#11926301

Splittings

SylowC19 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic19
commutatorC4×C19C2×C42
FrattiniC22×C4C22×D19
FittingC22×M16×C19C2
socleC22×C19#95
prime radicalC24×C19D4
cosocleC22×C4×C19C23
hypercenterC22×M16D19
hypocenterC19C2×H(3,ℤ/4)
LCSG ▷ C4×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×M16

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18069670, #18069672, #18069676, …
maximal normal subgroup of#18069670, #18069672, #18069676, …
maximal quotient ofC2×#14561463, #18071937, #18071940, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 4211);