Finite Group Databasebeta

#127×C461 #28414006

order14752
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C461 · Schur multiplier (H2) = C22×C4

Aliases

direct product#127×C461

Subgroups

subgroupG/H
center, socleC22×C461C23
commutator, Frattini, cosocleC22C23×C461
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C461 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

Conjugacy classes & character table

6454 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44441820, #44441869, #44442243, …
maximal subgroup of#331×C461, #353×C461, #453×C461, …
maximal normal subgroup of#331×C461, #353×C461, #453×C461, …
maximal quotient of#384×C461, #390×C461, #392×C461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14752, 34);