Finite Group Databasebeta

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#135×C373 #26045688

order11936
nilpotency class3
isoclinismisoclinic class of D8
automorphism?
homologyAbelianization (H1) = C23×C373 · Schur multiplier (H2) = C22

Aliases

direct product#135×C373

Subgroups

subgroupG/H
centerC4×C373D4
commutator, Frattini, cosocleC4C23×C373
socleC2×C373C2×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C373 ◁ C2×C4×C373 ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5222 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#37559229, #37559232, #37559539, …
maximal subgroup of#359×C373, #360×C373, #443×C373, …
maximal normal subgroup of#359×C373, #360×C373, #443×C373, …
maximal quotient of#416×C373, #427×C373, C4×D8×C373, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 42);