Finite Group Databasebeta

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#382×C293 #34035643

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C4×C293 · Schur multiplier (H2) = C22×C4

Aliases

direct product#382×C293

Subgroups

subgroupG/H
center, socle, prime radicalC23×C293C23
commutatorC22C22×C4×C293
Frattini, cosocleC23C23×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C293 ◁ G

154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

8204 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49156643, #49156666, #49156729, …
maximal subgroup of#1286×C293, #1295×C293, #1324×C293, …
maximal normal subgroup of#1286×C293, #1295×C293, #1324×C293, …
maximal quotient of#1434×C293, C4⋊#95×C293, #1442×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 63);