Finite Group Databasebeta

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#382×C239 #29504286

order15296
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C4×C239 · Schur multiplier (H2) = C22×C4

Aliases

direct product#382×C239

Subgroups

subgroupG/H
center, socle, prime radicalC23×C239C23
commutatorC22C22×C4×C239
Frattini, cosocleC23C23×C239
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C239 ◁ G

154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

Conjugacy classes & character table

6692 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44482406, #44482429, #44482492, …
maximal subgroup of#1286×C239, #1295×C239, #1324×C239, …
maximal normal subgroup of#1286×C239, #1295×C239, #1324×C239, …
maximal quotient of#1434×C239, C4⋊#95×C239, #1442×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 63);