Finite Group Databasebeta

#552×C293 #34035813

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

Aliases

direct product#552×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
prime radicalC2×D4×C293C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49170614, #49170666, #49170800, …
maximal subgroup of#3296×C293, #3300×C293, #3310×C293, …
maximal normal subgroup of#3296×C293, #3300×C293, #3310×C293, …
maximal quotient of#2343×C293, #2344×C293, #2346×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 233);