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C22×C4⋊C4×C293 #34035774

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C23×C4×C293 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊C4×C293

Subgroups

subgroupG/H
center, socle, prime radicalC24×C293C22
commutatorC2C23×C4×C293
Frattini, cosocleC22C24×C293
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C24×C293 ◁ G

418 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#49157014, #49157017, #49157027, …
maximal subgroup ofC4⋊#95×C293, #1436×C293, #1439×C293, …
maximal normal subgroup ofC4⋊#95×C293, #1436×C293, #1439×C293, …
maximal quotient ofC22×#95×C293, C2×C4×C4⋊C4×C293, C2×#380×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 194);