Finite Group Databasebeta

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#382×C241 #29507231

order15424
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C4×C241 · Schur multiplier (H2) = C22×C4

Aliases

direct product#382×C241

Subgroups

subgroupG/H
center, socle, prime radicalC23×C241C23
commutatorC22C22×C4×C241
Frattini, cosocleC23C23×C241
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C241 ◁ G

154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

6748 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44505303, #44505326, #44505389, …
maximal subgroup of#1286×C241, #1295×C241, #1324×C241, …
maximal normal subgroup of#1286×C241, #1295×C241, #1324×C241, …
maximal quotient of#1434×C241, C4⋊#95×C241, #1442×C241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 63);