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#120×C313 #23756378

order10016
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C313 · Schur multiplier (H2) = C24

Aliases

direct product#120×C313

Subgroups

subgroupG/H
center, socleC22×C313C23
commutator, Frattini, cosocleC22C23×C313
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C313 ◁ G

130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4382 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAΣL(1,𝔽16)×C313, B(4,𝔽2)×C313, C2×#120×C313, …
maximal normal subgroup ofAΣL(1,𝔽16)×C313, B(4,𝔽2)×C313, C2×#120×C313, …
maximal quotient of#379×C313, #385×C313, #386×C313, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10016, 27);