Finite Group Databasebeta

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#125×C461 #28414004

order14752
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C461 · Schur multiplier (H2) = C2

Aliases

direct product#125×C461

Subgroups

subgroupG/H
center, socle, prime radicalC22×C461C23
commutator, Frattini, cosocleC22C23×C461
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C461 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#44441818, #44442373, #44442380, …
maximal subgroup of#330×C461, #478×C461, #479×C461, …
maximal normal subgroup of#330×C461, #478×C461, #479×C461, …
maximal quotient of#382×C461, #387×C461, #389×C461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14752, 32);