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C2×#95×C293 #34035636

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C2×C42×C293 · Schur multiplier (H2) = C25

Aliases

direct productC2×#95×C293

Subgroups

subgroupG/H
center, socle, prime radicalC24×C293C22
commutatorC2C2×C42×C293
Frattini, cosocleC23C23×C293
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C24×C293 ◁ G

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

11720 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49156628, #49156664, #95×Dic293, …
maximal subgroup of#1280×C293, #1294×C293, C4×#95×C293, …
maximal normal subgroup of#1280×C293, #1294×C293, C4×#95×C293, …
maximal quotient ofC4×#95×C293, C22⋊#95×C293, C4⋊#95×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 56);