Finite Group Databasebeta

C2×#125×C293 #34035788

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

Aliases

direct productC2×#125×C293

Subgroups

subgroupG/H
center, socle, prime radicalC23×C293C23
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C293 ◁ G

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

8204 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49157141, C2×#34035871, #49157387, …
maximal subgroup of#1470×C293, C2×#330×C293, #1528×C293, …
maximal normal subgroup of#1470×C293, C2×#330×C293, #1528×C293, …
maximal quotient ofC2×#382×C293, C2×#387×C293, C2×#389×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 208);