Finite Group Databasebeta

#127×C457 #28410440

order14624
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C457 · Schur multiplier (H2) = C22×C4

Aliases

direct product#127×C457

Subgroups

subgroupG/H
center, socleC22×C457C23
commutator, Frattini, cosocleC22C23×C457
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C457 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7312

Conjugacy classes & character table

6398 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44416521, #44416570, #44416944, …
maximal subgroup of#331×C457, #353×C457, #453×C457, …
maximal normal subgroup of#331×C457, #353×C457, #453×C457, …
maximal quotient of#384×C457, #390×C457, #392×C457, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14624, 34);