Finite Group Databasebeta

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#562×C239 #29504466

order15296
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C24

Aliases

direct product#562×C239

Subgroups

subgroupG/H
center, socleC22×C239C24
commutator, Frattini, cosocleC22C24×C239
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C239 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7648

Conjugacy classes & character table

4541 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44483841, #44483865, #44483871
maximal subgroup of#1656×C239, #1661×C239, #1662×C239, …
maximal normal subgroup of#1656×C239, #1661×C239, #1662×C239, …
maximal quotient of#2376×C239, #2377×C239, #2378×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 243);