Finite Group Databasebeta

#555×C241 #29507404

order15424
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C241 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C241

Subgroups

subgroupG/H
center, socleC22×C241C24
commutator, Frattini, cosocleC22C24×C241
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C241 ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7712

Conjugacy classes & character table

6025 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44506528, #44506590, #44506673, …
maximal subgroup of#1624×C241, #1634×C241, #1646×C241, …
maximal normal subgroup of#1624×C241, #1634×C241, #1646×C241, …
maximal quotient of#2346×C241, #2354×C241, #2363×C241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 236);