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H(3,𝔽4)×C293 #34035822

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C22×C42

Aliases

direct productH(3,𝔽4)×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

5567 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49158074, #49158091, #49160786, …
maximal subgroup of#1655×C293, #1659×C293, #2199×C293, …
maximal normal subgroup of#1655×C293, #1659×C293, #2199×C293, …
maximal quotient of#2375×C293, #2379×C293, #2670×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 242);