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#384×C233 #28415951

order14912
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C4×C233 · Schur multiplier (H2) = C22×C4

Aliases

direct product#384×C233

Subgroups

subgroupG/H
center, socle, prime radicalC23×C233C23
commutatorC22C22×C4×C233
Frattini, cosocleC23C23×C233
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C233 ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14912

Conjugacy classes & character table

6524 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44449693, #44449756
maximal subgroup of#1296×C233, #1325×C233, #1802×C233, …
maximal normal subgroup of#1296×C233, #1325×C233, #1802×C233, …
maximal quotient ofC4⋊#95×C233, #1444×C233, #1842×C233, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 65);