Finite Group Databasebeta

#550×C241 #29507399

order15424
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C241 · Schur multiplier (H2) = C25

Aliases

direct product#550×C241

Subgroups

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

312 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#44506510, #44506572, #44506638, …
maximal subgroup of#1621×C241, #1631×C241, #1641×C241, …
maximal normal subgroup of#1621×C241, #1631×C241, #1641×C241, …
maximal quotient of#2341×C241, Q8×C4⋊C4×C241, #2354×C241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 231);