Finite Group Databasebeta

#121×Dic19 #14566149

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

Aliases

direct product#121×Dic19

Splittings

SylowC19 ⋊ C4×#121

Subgroups

subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
Fitting, prime radicalC2×C19×#121C2
socle, cosocleC23×C19C24
hypercenterC2×#121D19
hypocenterC19C4×#121
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#327×Dic19, #18073425, #18073435, …
maximal normal subgroup of#327×Dic19, #18073425, #18073435, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7024);