Finite Group Databasebeta

C2×#11926561 #14572177

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11926561

Splittings

SylowC19 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D19
commutatorC4×C19C23×C4
FrattiniC2×C4C23×D19
Fitting, prime radicalC22×#41×C19C2
socleC22×C19C2×C22⋊C4
cosocleC2×C4×C19C24
hypercenterC22×#41D19
hypocenterC19C2×#421
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

772 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#18088003, #18088005, #18088008, …
maximal normal subgroup of#18088003, #18088005, #18088008, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 13052);