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C2×2−1+4×C293 #34035845

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C25×C293 · Schur multiplier (H2) = C29

Aliases

direct productC2×2−1+4×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC2C25×C293
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

9962 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49158744, #49158760, #49167249, …
maximal subgroup of#1793×C293, #1796×C293, #2884×C293, …
maximal normal subgroup of#1793×C293, #1796×C293, #2884×C293, …
maximal quotient ofC2×#519×C293, C2×#520×C293, C4×2−1+4×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 265);