Finite Group Databasebeta

#537×C241 #29507386

order15424
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C241 · Schur multiplier (H2) = C25

Aliases

direct product#537×C241

Subgroups

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

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7712

Conjugacy classes & character table

5302 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44506380, #44506414, #44506448, …
maximal subgroup of#1598×C241, #1604×C241, #1610×C241, …
maximal normal subgroup of#1598×C241, #1604×C241, #1610×C241, …
maximal quotient of#2311×C241, #2316×C241, #2323×C241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 218);