Finite Group Databasebeta

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#382×C283 #31825979

order18112
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C4×C283 · Schur multiplier (H2) = C22×C4

Aliases

direct product#382×C283

Subgroups

subgroupG/H
center, socle, prime radicalC23×C283C23
commutatorC22C22×C4×C283
Frattini, cosocleC23C23×C283
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C283 ◁ G

154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18112

Conjugacy classes & character table

7924 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49119119, #49119142, #49119205, …
maximal subgroup of#1286×C283, #1295×C283, #1324×C283, …
maximal normal subgroup of#1286×C283, #1295×C283, #1324×C283, …
maximal quotient of#1434×C283, C4⋊#95×C283, #1442×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 63);