Finite Group Databasebeta

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#557×C293 #34035818

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

Aliases

direct product#557×C293

Subgroups

subgroupG/H
center, socle, prime radicalC22×C293C24
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

7325 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49157881, #49157943, #49158027, …
maximal subgroup of#1626×C293, #1636×C293, #1648×C293, …
maximal normal subgroup of#1626×C293, #1636×C293, #1648×C293, …
maximal quotient ofQ8×C4⋊C4×C293, #2351×C293, #2355×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 238);