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C2×H(5,𝔽2)×C293 #34035844

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

Aliases

direct productC2×H(5,𝔽2)×C293

Subgroups

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

898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49158733, #49158739, #49158755, …
maximal subgroup of#1790×C293, #1792×C293, #1795×C293, …
maximal normal subgroup of#1790×C293, #1792×C293, #1795×C293, …
maximal quotient ofC2×#518×C293, C2×#520×C293, C4×H(5,𝔽2)×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 264);